Grinding wheel grinding face gear tool setting method based on on-machine measurement

Abstract

The grinding wheel grinding face gear tool setting method based on on-machine measurement comprises the steps that an initial measurement coordinate system of a face gear is established; a face gear manufacturing error is considered, and a measurement coordinate system of the face gear is optimized through an iteration method; based on errors such as tooth profile, tooth pitch and tooth thickness of the face gear, a face gear tooth surface uniform grinding optimization model is established, the position of the measurement coordinate system is further optimized by adopting a nonlinear optimization method, and a final measurement coordinate system is obtained; and finally, determining the position of the grinding wheel grinding face gear according to the basic model of the grinding wheel grinding face gear. The tool setting precision and efficiency of the grinding wheel and the face gear can be improved, and the uniformity of the tooth surface grinding amount of the face gear can also be improved.

Description

Technical Field

[0001] The present invention relates to the technical field of gear tool setting, and particularly relates to a method for setting a face gear with respect to a grinding wheel of a grinding wheel based on in-machine measurement. Background Art

[0002] Face gear transmission is a meshing transmission between an involute cylindrical gear and a face gear. Compared with bevel gear transmission, face gear transmission has the advantages of compact structure, small volume, light weight, no axial positioning requirement, high load-carrying capacity, low noise, etc., and is widely used in the fields of aerospace, new energy vehicles, etc.

[0003] High-precision face gears need to be ground. After clamping the face gear on a numerical control machine tool, it is necessary to determine the initial positional relationship between the face gear and the grinding wheel before grinding. At present, the method of manually setting the tool is generally used to determine the initial positional relationship between the face gear and the grinding wheel, which not only has low tool setting efficiency, but also has low tool setting accuracy, and is prone to problems such as uneven tooth surface grinding amount; moreover, it is also prone to problems such as tool collision and fire, and part scrapping. Summary of the Invention

[0004] The present invention aims to at least solve one of the technical problems existing in the prior art. For this purpose, the present invention provides a method for setting a face gear with respect to a grinding wheel of a grinding wheel based on in-machine measurement, which not only has higher tool setting efficiency, but also has higher tool setting accuracy, and can reduce problems such as uneven tooth surface grinding amount.

[0005] According to an embodiment of the present invention, a method for setting a face gear with respect to a grinding wheel of a grinding wheel based on in-machine measurement includes:

[0006] S100. Measuring the coordinate point information of the tooth top surface and the outer peripheral surface of the face gear, and based on the tool setting principle when the grinding wheel grinds the face gear, establishing the initial measurement coordinate system S of the face gear cm ;

[0007] S200. Obtaining the theoretical measurement points on the theoretical tooth surface of the face gear, and in the initial measurement coordinate system S cm , touching the theoretical measurement points along the normal vector of the theoretical measurement points to obtain the actual measurement points on the actual tooth surface of the face gear, and judging the distance value between the theoretical measurement points and the actual measurement points;

[0008] S300. If the distance value is greater than a preset value, rotating the initial measurement coordinate system S cm around its own z cm axis by a certain angle, and repeating step S200 until the distance value is less than or equal to the preset value, and taking the rotated and adjusted measurement coordinate system S cm as the optimized measurement coordinate system S cm ;

[0009] S400. Calculate the tooth thickness error and the cumulative pitch tolerance of the face gear in the optimized measurement coordinate system S cm ;

[0010] S500. Convert the tooth thickness error and the cumulative pitch tolerance into tooth profile errors, and considering that when the optimized measurement coordinate system S cm rotates around its own z cm axis by different angles, the grinding allowances of each tooth surface of the face gear are different, establish the tooth profile error equation of the face gear;

[0011] S600. Optimize the tooth profile error equation to obtain an optimization objective function for the difference between the total tooth profile error value of all the left tooth surfaces and the total tooth profile error value of all the right tooth surfaces of the face gear. When solving the optimization objective function to be the minimum value, the angle by which the optimized measurement coordinate system S cm needs to rotate to obtain the final measurement coordinate system S cm ;

[0012] S700. Determine the tool setting position of the face gear according to the final measurement coordinate system S cm .

[0013] According to the on-machine measurement-based tool setting method for grinding a face gear according to an embodiment of the present invention, it has at least the following beneficial effects:

[0014] In the present invention, first, according to the coordinate point information of the tooth top surface and the outer peripheral surface of the face gear, an initial measurement coordinate system of the face gear is established. Then, considering the manufacturing error of the face gear, the initial measurement coordinate system is rotated, and the initial measurement coordinate system is optimized by an iterative method to obtain an optimized measurement coordinate system. After that, the cumulative pitch tolerance and the tooth thickness error of the face gear are calculated. Then, the tooth thickness error and the cumulative pitch tolerance are converted into tooth profile errors, and considering that when the optimized measurement coordinate system rotates by different angles, the grinding allowances of each tooth surface of the face gear are different, the tooth profile error equation of the face gear is established. Then, the tooth profile error equation is optimized to obtain an optimization objective function for the difference between the total tooth profile error value of all the left tooth surfaces and the total tooth profile error value of all the right tooth surfaces of the face gear. When solving the optimization objective function to be the minimum value, the angle by which the optimized measurement coordinate system S cm needs to rotate to obtain the final measurement coordinate system S cm . Finally, according to the final measurement coordinate system S cm , the tool setting position of the face gear can be accurately determined. According to the on-machine measurement-based tool setting method for grinding a face gear according to an embodiment of the present invention, not only is the tool setting efficiency higher, but also the tool setting accuracy is higher, which can reduce problems such as uneven grinding amounts of the tooth surfaces of the face gear, making the quality of the processed face gear higher.

[0015] According to some embodiments of the present invention, coordinate point information of the tooth top surface and the outer peripheral surface of the face gear is measured, and based on the tool setting principle when grinding the face gear with a grinding wheel, the initial measurement coordinate system S of the face gear is established cm , including:

[0016] Touch and measure n1 first points on the tooth top surface A1 of the face gear to obtain the coordinates of the n1 first points in the machine tool coordinate system;

[0017] According to the coordinates of the n1 first points, obtain the numerical value z of the coordinate origin of the initial measurement coordinate system S of the face gear cm in the z-axis direction of the machine tool coordinate system ocm calculation equation;

[0018] Touch and measure n2 second points on the outer peripheral surface of the face gear to obtain the coordinates of the n2 second points in the machine tool coordinate system, expressed as:

[0019] P A2i =[x A2i y A2i z A2i 1] T , i = 1, 2,..., n2;

[0020] Fit the n2 second points into a cylindrical surface A2, and the fitting equation of the cylindrical surface A2 is expressed as:

[0021] (x - x0) 2 +(y - y0) 2 +(z - z0) 2 -[a(x - x0)+b(y - y0)+c(z - z0)] 2 =r 2 ,

[0022] where a, b, c, x0, y0, z0, r are all unknown parameters;

[0023] Construct the following fitting error equation:

[0024]

[0025] Let v = [v1, v2,..., v n2 T , solve the following least squares equation to obtain 7 unknowns,

[0026]

[0027] where the constraint conditions s and t ensure the uniqueness of the solution. Substitute the obtained solution into the fitting equation of the cylindrical surface A2 to obtain the axis equation of the cylindrical surface A2, expressed as: ​

[0028]

[0029] Simultaneous value z ocm By solving the calculation equation of and the axis equation of the cylindrical surface A2, the coordinates of the intersection point of the axis of the face gear and the tooth top surface A1 can be obtained, and thus the initial measurement coordinate system S of the face gear can be determined. cm The origin o of cm The position of.

[0030] According to some embodiments of the present invention, the coordinate point information of the tooth top surface and the outer peripheral surface of the face gear is measured, and based on the tool setting principle when grinding the face gear with a grinding wheel, the initial measurement coordinate system S of the face gear is established. cm , further comprising:

[0031] Preliminarily determine the x cm axis and y cm axis directions of the initial measurement coordinate system S of the face gear, and the specific steps are as follows: cm Touch and measure the coordinates of the center points of the left and right tooth surfaces of the face gear, expressed as:

[0032] P

[0033] = [x cr(l) y cr(l) z cr(l) 1] cr(l) , T ,

[0034] where P cr is the center point of the right tooth surface, and P cl is the center point of the left tooth surface side;

[0035] Then the coordinates of the middle point of the tooth body of the face gear are expressed as:

[0036]

[0037] Make the x cm axis of the initial measurement coordinate system S of the face gear pass through point P cm ; cen ;

[0038] According to the right-hand rule of the coordinate system, determine the y cm axis direction of the initial measurement coordinate system S of the face gear. cm

[0039] According to some embodiments of the present invention, obtain the theoretical measurement points on the theoretical tooth surface of the face gear, and touch and measure the theoretical measurement points along the normal vector of the theoretical measurement points in the initial measurement coordinate system S cm to obtain the actual measurement points on the actual tooth surface of the face gear, including:

[0040] Obtain the coordinates of the theoretical measurement points on the left and right theoretical tooth surfaces of the face gear, expressed as:

[0041] P br(l) =[x br(l) y br(l) z br(l) 1] T ,

[0042] Obtain the normal vector of the theoretical measurement point, expressed as:

[0043] n br(l) =[n xbr(l) n ybr(l) n zbr(l) 1] T ;

[0044] In the initial measurement coordinate system S cm , touch and measure the theoretical measurement point P br(l) along n br(l) , output the measurement result, and obtain the actual measurement point P mr(l) on the actual tooth surface of the face gear, expressed as:

[0045] P mr(l) =[x mr(l) y mr(l) z mr(l) 1] T .

[0046] According to some embodiments of the present invention, if the distance value is greater than the preset value, rotate the initial measurement coordinate system S cm around its own z cm axis by a certain angle, and repeat step S200 until the distance value is less than or equal to the preset value, and use the rotation-adjusted measurement coordinate system S cm as the optimized measurement coordinate system S cm , including:

[0047] If the distance value is greater than the preset value, rotate the initial measurement coordinate system S cm around its own z cm axis by angle, where

[0048]

[0049] Solve the theoretical measurement point P cm of the theoretical tooth surface of the face gear and the normal vector n after rotating the initial measurement coordinate system S br(l)＇ by br(l)＇ angle:

[0050]

[0051] Repeat step S200 until the distance value is less than or equal to the preset value, and use the measurement coordinate system S after rotational adjustment cm as the optimized measurement coordinate system S cm .

[0052] According to some embodiments of the present invention, under the optimized measurement coordinate system S cm , calculate the tooth thickness error and the limit cumulative pitch error of the face gear, including:

[0053] The tooth thickness error of the face gear is expressed as:

[0054]

[0055] where α qlr is the included angle of the actual tooth thickness of the face gear, α plr is the included angle of the theoretical tooth thickness of the face gear, x pbri and y pbri are the coordinate values of the tooth thickness measurement points on the theoretical right tooth surface of the face gear obtained by calculation, and N2 is the number of teeth of the face gear;

[0056] α qlr is expressed as:

[0057]

[0058] where x qbri and y qbri are the coordinate values of the tooth thickness measurement point Q bri on the actual right tooth surface of the face gear, x qbli and y qbli are the coordinate values of the tooth thickness measurement point Q bli on the actual left tooth surface of the face gear, and are all obtained by touch measurement based on the optimized measurement coordinate system S cm ;

[0059] α plr is expressed as

[0060]

[0061] where x pbli and y pbli are the coordinate values of the tooth thickness measurement point P bli on the theoretical left tooth surface of the face gear, and are all obtained by calculation;

[0062] The limit cumulative pitch error of the face gear is expressed as:

[0063]

[0064] Among them,

[0065]

[0066] According to some embodiments of the present invention, in the optimized measurement coordinate system S cm below, calculating the tooth thickness error and the cumulative pitch limit error of the face gear further includes:

[0067] Project one tooth surface of the face gear onto the x g of the theoretical coordinate system S g o g z g plane to obtain a projection plane, and mesh the part of the projection plane corresponding to the working area of the tooth surface to obtain a measurement grid;

[0068] For any measurement point P ij (i = 1, 2, 3,..., m, j = 1, 2,..., n) on the measurement grid, in the z g axis direction of the theoretical coordinate system S g the value is z i , in the radial direction of the face gear the value is r i , the theoretical coordinates of the measurement point P ij are (x ij , y ij , z ij ), then there is:

[0069]

[0070] Simultaneously solve this formula and the tooth surface equation of the theoretical face gear to obtain the theoretical coordinate values of the measurement point P ij ;

[0071] According to the solution method of the theoretical coordinate values of the measurement point P ij , obtain the coordinate values of the pitch measurement point P br(l)1 of one theoretical tooth surface of the face gear as (x br(l)1 , y br(l)1 , z br(l)1 ), then the coordinate values of the pitch measurement point P bi of the i-th theoretical tooth surface are:

[0072]

[0073] Take the pitch measurement points of the theoretical tooth surface as the tooth thickness measurement points of the theoretical tooth surface.

[0074] According to some embodiments of the present invention, converting the tooth thickness error and the cumulative pitch limit error into tooth profile error, and considering the optimized measurement coordinate system S cm When rotating by different angles around its own z cm axis, the grinding allowances of each tooth surface of the face gear are different. Establishing the tooth profile error equation of the face gear includes:

[0075] Converting the tooth thickness error and the cumulative pitch limit error into tooth profile error, and considering the optimized measurement coordinate system S cm When rotating by different angles around its own z cm axis, the grinding allowances of each tooth surface of the face gear are different. Establishing the calculation formula for the coordinate values of the tooth profile measurement points on the actual tooth surface of the face gear, expressed as:

[0076] Z ij = M p · M t · M z · Q ij (i = 1, 2,..., m, j = 1, 2,..., n),

[0077] where, M p is the pitch error matrix of the face gear, expressed as:

[0078]

[0079] M t is the tooth thickness error matrix of the face gear, expressed as:

[0080]

[0081] M z is the grinding allowance optimization matrix of the face gear, expressed as:

[0082]

[0083] In the formula, φ fy represents the angle of rotation of the optimized measurement coordinate system S cm around its own z cm axis;

[0084] The tooth profile error equation of the face gear is expressed as:

[0085] ez ij = (Z ij - P ij ) · n ij ,(i = 1, 2,..., m, j = 1, 2,..., n),

[0086] In the formula, n ijis the unit normal vector of the theoretical tooth surface of the face gear.

[0087] According to some embodiments of the present invention, the tooth profile error equation is optimized to obtain an optimization objective function for the difference between the total tooth profile error value of all the left tooth surfaces of the face gear and the total tooth profile error value of all the right tooth surfaces, including:

[0088] The tooth profile error equation is optimized to obtain an optimization objective function, expressed as:

[0089]

[0090] where f z is the total tooth profile error value of the left tooth surface of the face gear, expressed as:

[0091]

[0092] f y is the total tooth profile error value of the right tooth surface of the face gear, expressed as:

[0093]

[0094] where the variable k represents the number of teeth measured of the face gear.

[0095] According to some embodiments of the present invention, when solving for the minimum value of the optimization objective function, the angle by which the optimized measurement coordinate system S cm needs to be rotated to obtain the final measurement coordinate system S cm , including:

[0096] The optimization objective function is expanded by quadratic Taylor series and transformed into a trust region subproblem for solution:

[0097]

[0098] where d is the optimal step length of iteration, Q k is the value of the model Q at the k-th iteration, and are the first-order derivative and the second-order derivative respectively;

[0099] Express as g k , express using the approximate Hessian matrix B k for representation, and adopt the Dog-leg search method for solution:

[0100]

[0101] s.t. ||d|| ≤ ρ k

[0102] Among them, ρ k is the trust region radius, and s and t are constraints;

[0103] The solution to the trust region problem can be given as:

[0104]

[0105] Among them, C is the Cauchy step length, which is obtained from the following equation:

[0106]

[0107] GN is the Gauss-Newton step length, which is obtained from the following equation:

[0108] GN = -(B k ) -1 g k ,

[0109] τ is solved from the following scalar equation:

[0110] ||-C + (τ - 1)·(GN + C)|| 2 = ρ k ,

[0111] and η k is used to measure the approximation degree of the equation, and η k is expressed as:

[0112]

[0113] Among them, Δ k is the value of the optimization variable at the k-th iteration. It is set that when 0.9 < η k ≤ 1, the trust region radius ρ k is increased; when 0.1 < η k ≤ 0.9, the trust region radius ρ k remains unchanged; when η k ≤ 0.1, the trust region radius ρ k is decreased.

[0114] Other features and advantages of the present invention will be described in the subsequent specification, and, in part, will become obvious from the specification or will be understood by implementing the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0115] The above and / or additional aspects and advantages of the present invention will become obvious and easy to understand from the description of the embodiments in conjunction with the following drawings, where:

[0116] Figure 1 is a schematic diagram of the motion relationship of a worm wheel grinding face gear according to an embodiment of the present invention;

[0117] Figure 2 Schematic diagram of the tooth profile of the generating gear in the embodiment of the present invention;

[0118] Figure 3 For the z-axis and origin o of the measurement coordinate system for establishing the face gear in the embodiment of the present invention cm of the schematic diagram; cm ;

[0119] Figure 4 For the x-axis of the measurement coordinate system for establishing the face gear in the embodiment of the present invention cm of the schematic diagram;

[0120] Figure 5 Schematic diagram of the influence of tooth thickness error on the measurement coordinate system in the embodiment of the present invention;

[0121] Figure 6 Schematic diagram of the first iteration of the measurement coordinate system of the face gear in the embodiment of the present invention;

[0122] Figure 7 Iteration flowchart of the measurement coordinate system of the face gear in the embodiment of the present invention;

[0123] Figure 8 Schematic diagram of the measurement point planning of the face gear in the embodiment of the present invention;

[0124] Figure 9 Schematic diagram of the tooth profile error of the face gear in the embodiment of the present invention;

[0125] Figure 10 Schematic diagram of the tooth thickness measurement of the face gear in the embodiment of the present invention;

[0126] Figure 11 Schematic diagram of the tooth pitch measurement of the face gear in the embodiment of the present invention;

[0127] Figure 12 Schematic diagram of the second iteration of the measurement coordinate system of the face gear in the embodiment of the present invention. Detailed implementation manners

[0128] The embodiments of the present invention will be described in detail below. Examples of the embodiments are shown in the accompanying drawings, where the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary only for explaining the present invention and should not be construed as limiting the present invention.

[0129] In the description of the present invention, it should be understood that with respect to the orientation description, for example, the orientation or positional relationship indicated by up, down, etc. is based on the orientation or positional relationship shown in the drawings. This is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation to the present invention.

[0130] In the description of the present invention, "a plurality" means two or more. If there is a description of first and second, it is only for the purpose of distinguishing technical features and cannot be understood as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features or implicitly specifying the sequence relationship of the indicated technical features.

[0131] In the description of the present invention, unless otherwise clearly defined, words such as "set", "installed", "connected", etc. should be understood in a broad sense. Those skilled in the art can reasonably determine the specific meanings of the above words in the present invention in combination with the specific content of the technical solution.

[0132] Next, refer to Figures 1 to 12 Describe the in-machine measurement grinding wheel grinding face gear tool setting method according to an embodiment of the present invention.

[0133] To better describe the in-machine measurement grinding wheel grinding face gear tool setting method according to an embodiment of the present invention, the basic principle of tool setting when grinding a face gear with a grinding wheel is explained. Refer to Figure 1 The schematic diagram of the motion relationship of worm grinding wheel grinding face gear shown in s The coordinate system S s y s The plane is perpendicular to the axis of the generating gear, and the axis z s Is collinear with the axis of the generating gear; the coordinate system S w Is the worm grinding wheel coordinate system, and the axis z w Is collinear with the axis of the worm grinding wheel, x w z w The plane is parallel to the x s z s The plane, and the axis z w The included angle with the axis x s Is λ w ; the coordinate system S 20 Is the transition coordinate system, and the axis z 20 Is collinear with the axis of the face gear, and the axis x 20 Is collinear with the axis z s ; the coordinate system S g Is the theoretical coordinate system of the face gear, and the axis z g Is collinear with the axis of the face gear, and the axis x g Is parallel to the axis z s x g y gThe plane is coplanar with the top surface of the face gear; coordinate system S cm is the measurement coordinate system of the face gear; axis z w and axis x s has a height distance of E ws , axis y 20 is at a distance of E s from axis x 2s .

[0134] Axis deflection angle λ w is the angle between the axis of the worm grinding wheel and the coordinate axis x s , which belongs to the installation angle of the worm grinding wheel relative to the generating gear, and its value can be determined by the following formula:

[0135]

[0136] where N s is the number of teeth of the generating gear, r ps is the pitch circle radius of the generating gear, N w is the number of starts of the worm grinding wheel.

[0137] The tooth profile of the generating gear is a standard involute, as Figure 2 shown. In the coordinate system S s , the tooth surface equation of the generating gear can be expressed as:

[0138]

[0139] where r bs is the base circle radius of the involute of the generating gear, θ 0s is the angular parameter of the intersection point of the involute of the generating gear and the base circle, θ s and u s are involute tooth surface parameters, where the left tooth profile corresponds to the upper sign in ± in the formula, and the right tooth profile corresponds to the lower sign.

[0140] According to the involute equation of the generating gear, the unit normal vector of the tooth surface of the generating gear can be obtained as:

[0141]

[0142] Taking the grinding wheel as a worm grinding wheel as an example, the tooth surface of the worm grinding wheel is obtained by enveloping the generating gear, and the tooth surface equation of the worm grinding wheel can be expressed as:

[0143]

[0144] where, is the transformation matrix from the coordinate system S s to the coordinate system S w , is the relative velocity vector between the generating gear and the worm grinding wheel.

[0145] The tooth surface of the face gear is obtained by the envelope of the generating gear, and the theoretical tooth surface equation of the face gear can be obtained, which is expressed as:

[0146]

[0147] Wherein, is the coordinate system S s to the coordinate system S g transformation matrix, is the relative velocity vector of the generating gear and the face gear.

[0148] When grinding the face gear with a worm grinding wheel, it is necessary to determine the relative position between the worm grinding wheel and the face gear, that is, it is necessary to determine the positional relationship between the worm grinding wheel and the face gear in the same coordinate system.

[0149] Among them, the tooth surface equation of the worm grinding wheel in the theoretical coordinate system S g of the face gear can be expressed as:

[0150]

[0151] Wherein, M g20 is the coordinate transformation matrix from the coordinate system S 20 to the coordinate system S g , M 20s is the coordinate transformation matrix from the coordinate system S s to the coordinate system S 20 , M sw is the coordinate transformation matrix from the coordinate system S w to the coordinate system S s .

[0152] During the process of the worm grinding wheel enveloping the face gear, according to the coordinate transformation matrices M g20 , M 20s , M sw , it is necessary to determine the worm grinding wheel coordinate system S w , E ws and the theoretical coordinate system S g of the face gear. All other parameters are known values. The values of the worm grinding wheel coordinate systems S w and E ws can be obtained when dressing the worm grinding wheel with a diamond roller. It is only necessary to determine the face gear coordinate system S g , and during the actual machining of the face gear, it is only necessary to determine the measuring coordinate system S cm of the face gear to obtain the tool setting position of the face gear.

[0153] The in-machine measurement-based tool setting method for grinding a face gear with a grinding wheel according to an embodiment of the present invention includes, but is not limited to, the following steps:

[0154] S100. Measure the coordinate point information of the tooth top surface and the outer peripheral surface of the face gear, and establish the initial measurement coordinate system S of the face gear based on the tool setting principle when grinding the face gear with a grinding wheel. cm ;

[0155] S200. Obtain the theoretical measurement points on the theoretical tooth surface of the face gear, and touch the theoretical measurement points along the normal vector of the theoretical measurement points in the initial measurement coordinate system S cm to obtain the actual measurement points on the actual tooth surface of the face gear, and judge the distance value between the theoretical measurement points and the actual measurement points;

[0156] S300. If the distance value is greater than the preset value, rotate the initial measurement coordinate system S cm around its own z cm axis by a certain angle, and repeat step S200 until the distance value is less than or equal to the preset value. Take the measurement coordinate system S after rotation adjustment cm as the optimized measurement coordinate system S cm ;

[0157] S400. Calculate the tooth thickness error and the limit cumulative pitch error of the face gear in the optimized measurement coordinate system S cm ;

[0158] S500. Convert the tooth thickness error and the limit cumulative pitch error into tooth profile errors, and consider that the grinding allowances of each tooth surface of the face gear are different when the optimized measurement coordinate system S cm rotates around its own z cm axis by different angles, and establish the tooth profile error equation of the face gear;

[0159] S600. Optimize the tooth profile error equation to obtain the optimization objective function of the difference between the total tooth profile error values of all the left tooth surfaces and the total tooth profile error values of all the right tooth surfaces of the face gear. Solve the angle by which the optimized measurement coordinate system S cm needs to rotate when the optimization objective function is the minimum value, and obtain the final measurement coordinate system S cm ;

[0160] S700. Determine the tool setting position of the face gear according to the final measurement coordinate system S cm ;

[0161] The in-machine measurement-based tool setting method for grinding a face gear with a grinding wheel provided by the embodiments of the present invention has the following beneficial effects:

[0162] The on-machine measurement-based tool setting method for grinding face gears of the present invention first establishes an initial measurement coordinate system for the face gear based on the coordinate point information of the tooth top surface and the outer peripheral surface of the face gear. Then, considering the manufacturing errors of the face gear, the initial measurement coordinate system is rotated, and the initial measurement coordinate system is optimized by an iterative method to obtain an optimized measurement coordinate system. After that, the tooth pitch limit cumulative error and the tooth thickness error of the face gear are calculated. Then, the tooth thickness error and the tooth pitch limit cumulative error are converted into tooth profile errors, and considering that the grinding allowances of each tooth surface of the face gear are different when the optimized measurement coordinate system rotates at different angles, a tooth profile error equation for the face gear is established. After that, the tooth profile error equation is optimized to obtain an optimized objective function for the difference between the total tooth profile error value of all the left tooth surfaces of the face gear and the total tooth profile error value of all the right tooth surfaces of the face gear. When the optimized objective function is solved to be the minimum value, the optimized measurement coordinate system S cm The required rotation angle is obtained to get the final measurement coordinate system S cm , and finally, based on the final measurement coordinate system S cm , the tool setting position of the face gear can be accurately determined.

[0163] According to the on-machine measurement-based tool setting method for grinding face gears of the embodiments of the present invention, not only is the tool setting efficiency higher, but also the tool setting accuracy is higher, which can reduce problems such as uneven grinding amounts of the tooth surfaces of the face gear, making the quality of the processed face gear higher.

[0164] It should be noted that the measurement coordinate systems mentioned in the present invention are all on-machine measurement coordinate systems.

[0165] In some embodiments of the present invention, the coordinate point information of the tooth top surface and the outer peripheral surface of the face gear is measured, and based on the tool setting principle when grinding the face gear with a worm grinding wheel, an initial measurement coordinate system S cm for the face gear is established, including the following steps:

[0166] When performing tool setting for grinding face gears with a worm grinding wheel, it is necessary to accurately establish the measurement coordinate system S cm for the face gear. The face gears actually processed will inevitably have machining errors, including tooth profile, tooth thickness, tooth pitch and other errors. It is necessary to establish the measurement coordinate system S cm for the face gear relatively accurately before measuring these errors.

[0167] When establishing the measurement coordinate system of the face gear, the measurement coordinate system of the face gear should be made as consistent as possible with its theoretical coordinate system. However, during the actual measurement process, when establishing the measurement coordinate system by touching various points on the corresponding feature elements with a measuring ball and obtaining coordinate information, the contingency during touching and machining errors will affect the accurate establishment of the measurement coordinate system. For example, when performing the angular positioning of the face gear, it needs to be determined by the center point of the tooth surface of the face gear. However, when initially touching the midpoint of the tooth surface, it can only be judged subjectively by humans, with low accuracy. Therefore, the following strategy for establishing the measurement coordinate system is adopted in this paper.

[0168] First, determine the z cm direction of the measurement coordinate system S cm of the face gear. As Figure 3 shown, S m is the default coordinate system of the machine tool. In this coordinate system, manually touch and measure at least two first points on the top tooth surface A1 of the face gear. The machine tool uniformly touches multiple other regions through the rotation of the main shaft, a total of n1 first points (n1≥3). The coordinates of the first points can be expressed as:

[0169] P A1i =[x A1i y A1i z A1i 1] T ,i=1,2,...,n1,

[0170] According to the coordinates of the n1 first points, obtain the calculation equation of the value z cm of the coordinate origin of the initial measurement coordinate system S ocm of the face gear in the z-axis direction of the machine tool coordinate system:

[0171]

[0172] Secondly, determine the position of the z cm axis and the origin o cm position of the measurement coordinate system S cm of the face gear. As Figure 3 shown, measure n2 second points on the outer peripheral surface of the face gear, which are divided into at least two upper and lower layers, and can be expressed as:

[0173] P A2i =[x A2i y A2i z A2i 1] T ,i=1,2,...,n2,

[0174] Fit the n2 points into a cylindrical surface A2, and set its axis as z cmThe position of the axis is set, and the direction of the tooth top surface of the face gear is set to the positive direction. This method can avoid the situation where the face gear installation tilt error causes the actual measurement of an ellipse when measuring the outer circle, resulting in z cm The axis position is not established accurately. The fitting equation of the cylindrical surface A2 can be expressed as:

[0175] (x-x0) 2 +(y-y0) 2 +(z-z0) 2 -[a(x-x0)+b(y-y0)+c(z-z0)] 2 =r 2 ,

[0176] Among them, a, b, c, x0, y0, z0, r are unknown parameters;

[0177] Construct the following fitting error equation:

[0178]

[0179] Let v = [v1, v2, ..., v n2 ] T , solving the following least squares equation can get 7 unknowns,

[0180]

[0181] Among them, the constraints s and t ensure the uniqueness of the solution. Substituting the obtained solution into the fitting equation of the cylindrical surface A2, the axis equation of the cylindrical surface A2 can be obtained, which is expressed as:

[0182]

[0183] Simultaneous value z ocm The calculation equation of and the axis equation of the cylindrical surface A2 are used to obtain the coordinates of the intersection of the axis of the face gear and the tooth top surface A1, and the initial measurement coordinate system S of the face gear can be determined. cm Origin o cm location.

[0184] Next, the initial measurement coordinate system S of the face gear is preliminarily determined. cm x cm Axis and y cm Axis direction, the specific steps are as follows: Figure 4 As shown, manually operate the measuring ball to roughly touch the center point of the left and right tooth surfaces of the measuring face gear, and the coordinate point can be obtained:

[0185] P cr(l) =[x cr(l) y cr(l) z cr(l) 1] T ,

[0186] Among them, P cr is the center point of the right tooth surface of the face gear, and P cl is the center point of the left tooth surface of the face gear. Then the midpoint of the tooth body of the face gear can be expressed as:

[0187]

[0188] The initial measurement coordinate system x cm axis of the face gear passes through point P cen . According to the right-hand rule of the coordinate system, the y cm axis direction of the initial measurement coordinate system S cm of the face gear can be determined.

[0189] In some embodiments of the present invention, to obtain the theoretical measurement points on the theoretical tooth surface of the face gear, in the initial measurement coordinate system S cm , touch the theoretical measurement points along the normal vector of the theoretical measurement points to obtain the actual measurement points on the actual tooth surface of the face gear, including the following steps:

[0190] Since the measurement point data obtained by manual touch is not very accurate, and there are errors such as tooth thickness in the face gear, at this time, the x cm axis still has an error from the ideal x cm axis of the measurement coordinate system S cm . It is necessary to further accurately determine the x cm axis, as shown in Figure 5 .

[0191] Obtain the theoretical measurement points of the left and right tooth surfaces of the face gear in the ideal measurement coordinate system (the theoretical coordinate system of the face gear), that is, the theoretical measurement points on the theoretical tooth surface of the face gear. The theoretical measurement point P br(l) is expressed as:

[0192] P br(l) =[x br(l) y br(l) z br(l) 1] T ,

[0193] where r represents the right tooth surface and l represents the left tooth surface;

[0194] Obtain the normal vector of the theoretical measurement point, which is expressed as:

[0195] n br(l) =[n xbr(l) n ybr(l) n zbr(l) 1] T ;

[0196] Touch the theoretical measurement point P along n br(l) ​br(l) , as Figure 6 shown, output the measurement result to obtain the actual measurement point P of the actual tooth surface of the face gear mr(l) , expressed as:

[0197] P mr(l) = [x mr(l) y mr(l) z mr(l) 1] T ,

[0198] In some embodiments of the present invention, if the distance value is greater than the preset value, rotate the initial measurement coordinate system S cm around its own z cm axis by a certain angle, and repeat step S200 until the distance value is less than or equal to the preset value. Take the rotated and adjusted measurement coordinate system S cm as the optimized measurement coordinate system S cm , including the following steps:

[0199] If the distance value is greater than the preset value, rotate the initial measurement coordinate system S cm around its own z cm axis by angle, where

[0200]

[0201] Solve for the theoretical measurement point P of the tooth surface of the face gear after the initial measurement coordinate system S cm is rotated by angle, as well as the normal vector n br(l)＇ : br(l)＇ :

[0202]

[0203] Repeat step S200 until the distance value is less than or equal to the preset value. Take the rotated and adjusted measurement coordinate system S cm as the optimized measurement coordinate system S cm .

[0204] For example, iterate according to the Figure 7 process, set the preset value ε to 0.0001 mm, and stop the iteration until the distance value ≤ 0.0001 mm, then the precise establishment of the x cm axis of the measurement coordinate system of the face gear can be completed, thereby completing the optimization of the initial measurement coordinate system S cm .

[0205] In some embodiments of the present invention, under the optimized measurement coordinate system S cm , calculate the tooth thickness error and the pitch limit cumulative error of the face gear, including the following steps:

[0206] The tooth surface error of the face gear mainly includes errors in tooth shape, tooth pitch, tooth thickness, etc. Considering that the face gear is a complex curved surface in space, the tooth thickness error and the maximum cumulative error of the tooth pitch of the face gear can be calculated by the following method.

[0207] like Figure 8 As shown, one of the tooth surfaces of the face gear is projected onto the theoretical coordinate system S of the face gear. g x g o g z g The projection surface abcd is obtained on the plane, and the part a1b1c1d1 of the projection surface corresponding to the working area of the tooth surface is gridded by m×n to obtain a measurement grid. The upper and lower sides of the tooth height direction of the face gear are indented by h1 and h2 respectively, and the indentation amount exceeds 0.6mm, and generally h1 and h2 are equal; the inner diameter and outer diameter ends of the face gear in the radial direction are indented by w1 and w2 respectively, and the indentation amount exceeds 1mm, and generally w1 and w2 are equal; the midpoint of the grid is used as the measurement reference point, that is, the tooth profile error at this point is 0.

[0208] For any measurement point P on the measurement grid ij (i=1,2,3,…,m,j=1,2,…,n), in the theoretical coordinate system S g z g The axis direction is z i , the value in the radial direction of the face gear is r i , measuring point P ij The theoretical coordinates are (x ij ,y ij , z ij ), then:

[0209]

[0210] Solve this formula together with the tooth surface equation of the face gear to obtain the measurement point P ij Theoretical coordinate values.

[0211] For the calculation of tooth thickness error and pitch error of face gear, the midpoint of each tooth surface is the theoretical coordinate of the point to be measured. ij The theoretical coordinate value of the tooth pitch measurement point P of one of the theoretical tooth surfaces of the face gear is obtained by solving the theoretical coordinate value of the tooth pitch measurement point P of the face gear. br(l)1 The coordinate value of (x br(l)1 ,y br(l)1 , z br(l)1 ), taking clockwise as an example, the pitch measurement point P of the ith theoretical tooth surface is bi The coordinate values are:

[0212]

[0213] The tooth profile error of the face gear is the error value between the actual tooth surface and the theoretical tooth surface. As shown in Figure 9 it can be expressed as:

[0214] e ij =(Q ij -P ij )·n ij ,(i = 1, 2,..., m, j = 1, 2,..., n),

[0215] where Q ij is the coordinate value of the measurement point on the actual tooth surface of the face gear, P ij is the coordinate value of the measurement point on the theoretical tooth surface of the face gear, n ij is the unit normal vector of the theoretical tooth surface of the face gear, and N2 is the number of teeth of the face gear.

[0216] The tooth thickness error of the face gear is the error value between the theoretical tooth thickness and the actual tooth thickness. As shown in Figure 10 it can be expressed as:

[0217]

[0218] where α qlr is the included angle of the actual tooth thickness of the face gear, α plr is the included angle of the theoretical tooth thickness of the face gear, x pbri and y pbri are the coordinate values of the tooth thickness measurement points on the theoretical right tooth surface of the face gear obtained by calculation, and N2 is the number of teeth of the face gear;

[0219] α qlr is expressed as:

[0220]

[0221] where x qbri and y qbri are the coordinate values of the tooth thickness measurement point Q bri on the actual right tooth surface of the face gear, x qbli and y qbli are the coordinate values of the tooth thickness measurement point Q bli on the actual left tooth surface of the face gear, both obtained by touch measurement based on the optimized measurement coordinate system S cm ;

[0222] Q bri can be expressed as:

[0223] Q bri =[x qbri y qbri z qbri 1] T ,

[0224] Qbli Can be expressed as:

[0225] Q bli = [x qbli y qbli z qbli 1] T ,

[0226] α plr Is expressed as:

[0227]

[0228] Wherein, x pbli And y pbli Are the coordinate values of the tooth thickness measurement point P of the theoretical left tooth surface of the face gear obtained by calculation; bli Of;

[0229] P bri Can be expressed as:

[0230] P bri = [x pbri y pbri z pbri 1] T ,

[0231] P bli Can be expressed as:

[0232] P bli = [x pbli y pbli z pbli 1] T 。

[0233] As Figure 11 Shown, the tooth pitch error of the face gear is the error between the theoretical and actual values on the same side tooth surface of two adjacent teeth. The tooth pitch measurement point of the face gear is usually the reference point of the tooth surface, that is, the tooth thickness measurement point of the face gear. The included angle between two adjacent tooth pitch measurement points in the horizontal plane is equal to the included angle between two vectors, that is:

[0234]

[0235] Then the tooth pitch limit cumulative error of the face gear can be expressed as:

[0236]

[0237] In some embodiments of the present invention, referring to Figure 11 Shown, the tooth thickness error and the tooth pitch limit cumulative error are converted into tooth profile errors, and the optimized measurement coordinate system S cm Rotates around its own z cmWhen the shaft rotates at different angles, the grinding allowances of the tooth surfaces of the face gear are different. To establish the tooth profile error equation of the face gear, the following steps are included:

[0238] Convert the tooth thickness error and the cumulative pitch limit error into tooth profile errors, and consider the optimized measurement coordinate system S cm Rotate around its own z cm When the shaft rotates at different angles, the grinding allowances of the tooth surfaces of the face gear are different. Establish the coordinate value calculation formula for the tooth profile measurement points of the actual tooth surface of the face gear, expressed as:

[0239] Z ij = M p ·M t ·M z ·Q ij (i = 1, 2,..., m, j = 1, 2,..., n),

[0240] where, M p is the pitch error matrix of the face gear, expressed as:

[0241]

[0242] M t is the tooth thickness error matrix of the face gear, expressed as:

[0243]

[0244] M z is the grinding allowance optimization matrix of the face gear, expressed as:

[0245]

[0246] In the formula, φ fy represents the angle of rotation of the optimized measurement coordinate system S cm around its own z cm axis;

[0247] The tooth profile error equation of the face gear is expressed as:

[0248] ez ij = (Z ij - P ij )·n ij ,(i = 1, 2,..., m, j = 1, 2,..., n),

[0249] In the formula, n ij is the unit normal vector of the theoretical tooth surface of the face gear.

[0250] Reference Figure 12, in some embodiments of the present invention, the tooth profile error equation is optimized to obtain an optimization objective function for the difference between the total tooth profile error of all the left tooth surfaces of the face gear and the total tooth profile error of all the right tooth surfaces, including the following steps:

[0251] Optimize the tooth profile error equation to obtain the optimization objective function, expressed as:

[0252]

[0253] where f z is the total tooth profile error of the left tooth surface of the face gear, expressed as:

[0254]

[0255] f y is the total tooth profile error of the right tooth surface of the face gear, expressed as:

[0256]

[0257] where the variable k represents the number of teeth measured on the face gear.

[0258] In some embodiments of the present invention, when solving for the minimum value of the optimization objective function, the angle by which the optimized measurement coordinate system S cm needs to be rotated to obtain the final measurement coordinate system S cm , including the following steps:

[0259] Perform a second-order Taylor expansion on the optimization objective function and transform it into a trust-region subproblem for solution:

[0260]

[0261] where d is the optimal step length of the iteration, Q k is the value of the model Q at the k-th iteration, and are the first-order derivative and the second-order derivative respectively;

[0262] Express as g k , express using the approximate Hessian matrix B k for representation, and use the Dog-leg search method to solve:

[0263]

[0264] s.t. ||d|| ≤ ρ k

[0265] where ρ k is the trust-region radius, and s and t are the constraint conditions;

[0266] The solution to the trust region problem can be given as:

[0267]

[0268] where C is the Cauchy step, obtained from the following equation:

[0269]

[0270] GN is the Gauss-Newton step, obtained from the following equation:

[0271] GN = -(B k ) -1 g k ,

[0272] τ is solved from the following scalar equation:

[0273] ||-C + (τ - 1)·(GN + C)|| 2 = ρ k ,

[0274] and η k is used to measure the approximation degree of the equation, η k is expressed as:

[0275]

[0276] where Δ k is the value of the optimization variable at the k-th iteration. It is set that when 0.9 < η k ≤ 1, the approximation degree is better, and the trust region radius ρ k is increased to increase the search step; when 0.1 < η k ≤ 0.9, the trust region radius ρ k remains unchanged; when η k ≤ 0.1, the trust region radius ρ k is decreased.

[0277] Through the above method, not only the tool setting time is shorter and the tool setting efficiency is higher, but also the final measurement coordinate system S cm of the face gear has high accuracy, thereby making the tool setting position of the face gear very accurate, being able to reduce problems such as uneven tooth surface grinding amount of the face gear, and making the quality of the face gear higher after machining.

[0278] The above has described the embodiments of the present invention in detail with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments, and various changes can be made without departing from the spirit of the present invention within the knowledge scope of those of ordinary skill in the art.

Claims

1. A method for tool setting of a grinding wheel for face gear based on in-machine measurement, characterized in that, It includes the following steps: S100. Measure the coordinate point information of the tooth top surface and the outer peripheral surface of the face gear, and establish the initial measurement coordinate system S of the face gear based on the tool setting principle when grinding the face gear with a grinding wheel cm ; S200. Obtain the theoretical measurement points on the theoretical tooth surface of the face gear, and under the initial measurement coordinate system S cm Touch the theoretical measurement points along the normal vector of the theoretical measurement points to obtain the actual measurement points on the actual tooth surface of the face gear, and judge the distance value between the theoretical measurement points and the actual measurement points; S300. If the distance value is greater than a preset value, rotate the initial measurement coordinate system S cm about its own z cm axis by a certain angle, and repeat step S200 until the distance value is less than or equal to the preset value. Then, use the measurement coordinate system S cm after the rotation adjustment as the optimized measurement coordinate system S cm ; S400. Calculate the tooth thickness error and the limit cumulative pitch error of the face gear in the optimized measurement coordinate system S cm ; S500. Convert the tooth thickness error and the cumulative pitch limit error into tooth profile errors, and consider the optimized measurement coordinate system S cm Rotate around its own z cm When rotating at different angles around the axis, the grinding allowances of the tooth surfaces of the face gear are different, and establish the tooth profile error equation of the face gear; Optimize the tooth profile error equation to obtain an optimized objective function for the difference between the total tooth profile error of all left tooth surfaces and the total tooth profile error of all right tooth surfaces of the face gear. When solving the optimized objective function to be the minimum value, the optimized measurement coordinate system S cm The required rotation angle is obtained to get the final measurement coordinate system S cm ; S700. Determine the tool setting position of the face gear according to the final measurement coordinate system S cm , and determine the tool setting position of the face gear.

2. The on-machine measurement-based tool setting method for a grinding wheel and face gear according to claim 1, wherein The coordinate point information of the tooth top surface and the outer peripheral surface of the face gear is measured, and based on the tool setting principle when grinding the face gear with a grinding wheel, the initial measurement coordinate system S of the face gear is established cm , including: Touch n1 first points on the top face A1 of the face gear teeth to obtain the coordinates of the n1 first points in the machine tool coordinate system; Based on the coordinates of the n1 first points, obtain the initial measurement coordinate system S of the face gear cm The value z of the coordinate origin of ocm in the z-axis direction of the machine tool coordinate system; Calculation equation; Touch n2 second points on the outer peripheral face of the face gear to obtain the coordinates of the n2 second points in the machine tool coordinate system, expressed as: P A2i = [x A2i y A2i z A2i 1] T , i = 1, 2,..., n2; Fit the n2 second points into a cylindrical surface A2, and the fitting equation of the cylindrical surface A2 is expressed as: (x - x0) 2 +(y - y0) 2 +(z - z0) 2 -[a(x - x0)+b(y - y0)+c(z - z0)] 2 =r 2 , where a, b, c, x0, y0, z0, and r are all unknown parameters; Construct the following fitting error equation: Let \(v = [v_1, v_2, \ldots, v n2 T , and solving the following least - squares equation can obtain the seven unknowns,​ where the constraint conditions s and t ensure the uniqueness of the solution. Substitute the obtained solution into the fitting equation of the cylindrical surface A2 to obtain the axis equation of the cylindrical surface A2, expressed as: Simultaneous numerical value z ocm By solving the calculation equation of and the axis equation of the cylindrical surface A2, the coordinates of the intersection point of the axis of the face gear and the tooth top surface A1 can be obtained, and thus the origin o cm of cm can be determined.​ 3. The on-machine measurement-based gear alignment method for a gear grinding wheel according to claim 2, characterized in that The coordinate point information of the tooth top surface and the outer peripheral surface of the face gear is measured, and based on the tool setting principle when grinding the face gear with a grinding wheel, the initial measurement coordinate system S of the face gear is established cm , further comprising: Preliminarily determine the initial measurement coordinate system S of the face gear cm for the x cm axis and the y cm axis directions. The specific steps are as follows: Touch the coordinates of the center points of the left and right tooth faces of the face gear, expressed as: P cr(l) = [x cr(l) y cr(l) z cr(l) 1] T , Among them, P cr is the center point of the right tooth surface of the face gear, and P cl is the center point of the left tooth surface of the face gear; Then the coordinates of the middle point of the tooth body of the face gear are expressed as: Make the x-axis of the initial measurement coordinate system S of the face gear pass through point P cm x cm axis cen ; According to the right-hand rule of the coordinate system, determine the initial measurement coordinate system S of the face gear cm in the y cm axis direction.

4. The on-machine measurement-based tool setting method for grinding face gears with a grinding wheel according to claim 3, wherein, Obtaining the theoretical measurement points on the theoretical tooth surface of the face gear, in the initial measurement coordinate system S cm Touching the theoretical measurement points along the normal vector of the theoretical measurement points to obtain the actual measurement points on the actual tooth surface of the face gear, including: Obtain the coordinates of the theoretical measurement points of the left and right theoretical tooth faces of the face gear, expressed as: P br(l) = [x br(l) y br(l) z br(l) 1] T , Obtain the normal vector of the theoretical measurement points, expressed as: n br(l) = [n xbr(l) n ybr(l) n zbr(l) 1] T ; In the initial measurement coordinate system S cm along n br(l) touch and measure the theoretical measurement point P br(l) output the measurement result to obtain the actual measurement point P on the actual tooth surface of the face gear mr(l) which is expressed as: P mr(l) = [x mr(l) y mr(l) z mr(l) 1] T 。 5. The on-machine measurement-based tool setting method for grinding face gears with a grinding wheel according to claim 4, characterized in that If the distance value is greater than a preset value, rotate the initial measurement coordinate system S cm around its own z cm axis by a certain angle, and repeat step S200 until the distance value is less than or equal to the preset value. Then, use the rotation-adjusted measurement coordinate system S cm as the optimized measurement coordinate system S cm , including: If the distance value is greater than the preset value, rotate the initial measurement coordinate system S cm about its own z cm axis by an angle, where Solve for the initial measurement coordinate system S cm Rotate After the angle, the theoretical measurement point P of the theoretical tooth surface of the face gear br(l)＇ And the normal vector n br(l)＇ : Repeat step S200 until the distance value is less than or equal to the preset value, and use the measurement coordinate system S after rotational adjustment cm as the optimized measurement coordinate system S cm .

6. The on-machine measuring-based tool setting method for a grinding wheel and face gear according to claim 1, characterized in that Under the optimized measurement coordinate system S cm calculate the tooth thickness error and the limit cumulative pitch error of the face gear, including: The tooth thickness error of the face gear is expressed as: Among them, α qlr is the included angle of the actual tooth thickness of the face gear, α plr is the included angle of the theoretical tooth thickness of the face gear, x pbri and y pbri are the coordinate values of the tooth thickness measurement points on the theoretical right tooth surface of the face gear obtained by calculation, and N2 is the number of teeth of the face gear; α qlr Expressed as: where x qbri and y qbri are the coordinate values of the tooth thickness measurement point Q bri on the actual right tooth surface of the face gear, and x qbli and y qbli are the coordinate values of the tooth thickness measurement point Q bli on the actual left tooth surface of the face gear, both obtained by touch measurement based on the optimized measurement coordinate system S cm ; α plr represented as Among them, x pbli and y pbli are the coordinate values of the tooth thickness measurement point P bli of the theoretical left tooth surface of the face gear obtained by calculation; The limit cumulative pitch error of the face gear is expressed as: where 7. The on-machine measurement-based tool setting method for grinding face gears with a grinding wheel according to claim 6, characterized in that In the optimized measurement coordinate system S cm calculate the tooth thickness error and the limit cumulative pitch error of the face gear, and further include: Project one of the tooth surfaces of the face gear onto the theoretical coordinate system S of the face gear g in the x g o g z g plane to obtain a projection plane, and mesh the part of the projection plane corresponding to the working area of the tooth surface to obtain a measurement mesh; For any measurement point P on the measurement grid ij (i = 1, 2, 3, …, m, j = 1, 2, …, n), in the theoretical coordinate system S g the value in the z g axis direction is z i , and the value in the radial direction of the face gear is r i , the theoretical coordinates of the measurement point P ij are (x ij , y ij , z ij ), then there is: Simultaneously solve this formula and the theoretical tooth surface equation of the face gear to obtain the theoretical coordinate values of the measurement point P ij ; According to the solution method of the theoretical coordinate value of the measurement point P ij obtain the coordinate value of the pitch measurement point P br(l)1 of one of the theoretical tooth surfaces of the face gear as (x br(l)1 , y br(l)1 , z br(l)1 ). Then the coordinate value of the pitch measurement point P bi of the i-th theoretical tooth surface is: Take the pitch measurement points of the theoretical tooth face as the tooth thickness measurement points of the theoretical tooth face.

8. The on-machine measurement-based tool setting method for grinding face gears with a grinding wheel according to claim 7, characterized in that Converting the tooth thickness error and the cumulative pitch limit error into tooth profile error, and considering the optimized measurement coordinate system S cm When rotating by different angles around its own z cm The grinding allowances of the tooth surfaces of the face gear are different, and a tooth profile error equation of the face gear is established, including: Convert the tooth thickness error and the cumulative pitch limit error into tooth profile errors, and consider the optimized measurement coordinate system S cm Rotate around its own z cm When rotating different angles around the axis, the grinding allowances of the tooth surfaces of the face gear are different. Establish a coordinate value calculation formula for the tooth profile measurement points of the actual tooth surface of the face gear, expressed as: Z ij = M p ·M t ·M z ·Q ij (i = 1, 2, ..., m, j = 1, 2, ..., n), Among them, M p is the pitch error matrix of the face gear, expressed as: M t is the tooth thickness error matrix of the face gear, expressed as: M z is the grinding allowance optimization matrix for the face gear, expressed as: In the formula, represents the optimized measurement coordinate system S cm rotating around its own z cm axis by an angle; The tooth profile error equation of the face gear is expressed as: ez ij = (Z ij - P ij ) · n ij , (i = 1, 2,..., m, j = 1, 2,..., n), where n ij is the unit normal vector of the theoretical tooth surface of the face gear.

9. The on-machine measurement-based method for tool setting of a grinding wheel for face gears according to claim 8, characterized in that Optimize the tooth profile error equation to obtain an optimization objective function for the difference between the total tooth profile error value of all the left tooth faces and the total tooth profile error value of all the right tooth faces of the face gear, including: Optimize the tooth profile error equation to obtain an optimization objective function, expressed as: where f z is the total tooth profile error of the left tooth surface of the face gear, expressed as: f y is the total tooth profile error of the right tooth surface of the face gear, expressed as: where the variable k represents the number of teeth measured for the face gear.

10. The on-machine measurement-based tool setting method for grinding face gears with a grinding wheel according to claim 9, wherein, When solving for the minimum value of the optimization objective function, the optimized measurement coordinate system S cm The required rotation angle to obtain the final measurement coordinate system S cm , including: Perform a second-order Taylor expansion on the optimization objective function and transform it into a trust-region subproblem for solution: where d is the optimal step size of the iteration, and Q k is the value of model Q at the k-th iteration, and are the first-order derivative and the second-order derivative respectively; Express as g k , and express using the approximate Hessian matrix B k , and solve it using the Dog-leg search method: such that ||d|| ≤ ρ k where ρ k is the trust region radius, and s and t are constraints; The solution to the trust-region problem can be given as: where C is the Cauchy step size, obtained from the following equation: GN is the Gauss-Newton step size, obtained from the following equation: GN = -(B k ) -1 g k , τ is solved from the following scalar equation: ||-C+(τ-1)·(GN+C)|| 2 = ρ k , and use η k to measure the approximation degree of the equation, where η k is expressed as: where, Δ k is the value of the optimization variable at the k-th iteration. It is set that when 0.9 < η k ≤ 1, the trust region radius ρ k is increased; when 0.1 < η k ≤ 0.9, the trust region radius ρ k remains unchanged; when η k ≤ 0.1, the trust region radius ρ k is decreased.

Images